Please use this identifier to cite or link to this item:
Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: The effect of seasonal host birth rates on population dynamics: the importance of resonance
Authors: Ireland, Jillian M
Norman, Rachel
Greenman, Jonathan
Contact Email:
Keywords: seasonality
mathematical model
infectious disease
Issue Date: 21-Nov-2004
Publisher: Elsevier
Citation: Ireland JM, Norman R & Greenman J (2004) The effect of seasonal host birth rates on population dynamics: the importance of resonance, Journal of Theoretical Biology, 231 (2), pp. 229-238.
Abstract: Many of the simple mathematical models currently in use often fail to capture important biological factors. Here we extend current models of insect-pathogen interactions to include seasonality in the birth rate. In particular, we consider the SIR model with self-regulation when applied to specific cases - - rabbit haemorrhagic disease and fox rabies. In this paper, we briefly summarize the results of the model with a constant time-independent birth rate, a, which we then replace with the time dependent birth rate a(t), to investigate how this effects the dynamics of the host population. We can split parameter space into an area in which the model without seasonality has no oscillations, in which case a simple averaging rule predicts the behaviour. Alternatively, in the area where oscillations to the equilibrium do occur in the non-seasonal model, disease persistence is more complicated and we get more complex dynamical behaviour in this case. We apply resonance techniques to discover the structure of the subharmonic modes of the SIR model with self-regulation. We then look at whether many biological systems are likely to display these "resonant" dynamics and find that we would expect them to be widespread.
Type: Journal Article
DOI Link:
Rights: The publisher does not allow this work to be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.
Affiliation: University of Stirling
Mathematics - CSM Dept
Mathematics - CSM Dept

Files in This Item:
File Description SizeFormat 
irelandetal04resonance.pdf280.87 kBAdobe PDFUnder Embargo until 31/12/2999     Request a copy

Note: If any of the files in this item are currently embargoed, you can request a copy directly from the author by clicking the padlock icon above. However, this facility is dependant on the depositor still being contactable at their original email address.

This item is protected by original copyright

Items in the Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

If you believe that any material held in STORRE infringes copyright, please contact providing details and we will remove the Work from public display in STORRE and investigate your claim.